Fixed set search applied to the traveling salesman problem

TL;DR

This paper introduces Fixed Set Search (FSS), a new metaheuristic that enhances solution quality for the Traveling Salesman Problem by focusing on common elements in high-quality solutions, outperforming existing methods.

Contribution

The paper presents FSS, a novel learning-based metaheuristic that improves upon GRASP by fixing solution elements, demonstrated effectively on the TSP.

Findings

FSS finds significantly better solutions than GRASP.

FSS outperforms the dynamic convexized method.

FSS is simple to implement and effective.

Abstract

In this paper we present a new population based metaheuristic called the fixed set search (FSS). The proposed approach represents a method of adding a learning mechanism to the greedy randomized adaptive search procedure (GRASP). The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near optimal solutions for the underlying subproblem. The simplicity of implementing the proposed method is illustrated on the traveling salesman problem. Our computational experiments show that the FSS manages to find significantly better solutions than the GRASP it is based on and also the dynamic convexized method.